Contact Analysis Between a Moving Solid and the Boundary of its Swept Volume

The modeling of many practical problems in design and manufacturing involving moving objects relies on sweeps and their boundaries, which are mathematically described by the envelopes to the family of shapes generated by the moving object. In many problems, such as the design and analysis of higher pairs or tool path planning, contact changes between the moving object and the boundary of its swept volume become critical because they often translate into functional changes of the system under consideration. However, the difficulty of this task quickly escalates beyond the reach of existing approaches as the complexity of the shape and motion increases. We recently proposed a sweep boundary evaluator for general sweeps in conjunction with efficient point sampling and surface reconstruction algorithms that relies on our novel point membership classification (PMC) test for general solid sweeps. In this paper we describe a new approach that automates the prediction of changes in the state of contact between a shape of arbitrary complexity moving according to an affine motion, and the boundary of its swept set. We show that we can predict when and where such contact changes occur with only minimal additional computational cost by exploiting the data output by our sweep boundary evaluator. We discuss the problem and the associated computational issues in a 2D framework, and we conclude by discussing the extension of our approach to 3D moving objects. Proceedings of ASME IDETC08 Design Automation Conference. New York, August 2008 Corresponding author. Department of Mechanical Engineering, Storrs, CT 06269-3139